Optimization of cross-section of hollow prismatic bars in torsion

Abstract

The problem of optimal shape design of a doubly connected prismatic bar in torsion is formulated and solved numerically by the ÿnite element method. The cost function is torsional rigidity of the domain, constraint is the constant area of the cross-section while shape parameters are co-ordinates of the ÿnite element nodes along the variable boundary. The variable boundary is either the inner or outer boundary of the domain. A dual problem of minimizing the area at the constant torsional rigidity is also considered. The problem is solved directly by optimizing the cost function with respect to the shape parameters. Numerical examples are given for two benchmark problems.

Torsion of moderately thick hollow tubes with polygonal shapes

“…The first one is governed by Poisson's equation and the second one by Laplace's equation, both with simple boundary conditions. For this purpose, the normalized stress function w ¼ / Ga is divided into two parts as follows (Mejak, 2000):…”

“…/j.mechrescom.2007 ized the method to treat arbitrary cross sections consisting of circular arcs and straight lines, all with a uniform thickness (Wang, 1998). Mejak (2000) presented a method for optimal shape design of doubly connected bars in torsion. He solved the problem numerically by the finite element method.…”

Asymptotic models for optimizing the contour of multiply-connected cross-section of an elastic bar in torsion

“…In the latter case, an exact solution of the optimization problem was obtained by Kurshin and Onoprienko (1976) using a complex variable technique. Finite element algorithms adjusted for structural shape optimization of elastic bars in torsion were suggested by Hou et al (1984) and Mejak (2000). Curtis and Walpole (1982) obtained an asymptotic solution of the three-dimensional optimization problem for an axisymmetric hollow shaft with a specified inner variable cross-section in the case of small shaft thickness.…”